Creeping flows through confined arrays of cylinders
Data files
Mar 20, 2026 version files 84.14 KB
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Experimental_flowrates_Figure2.csv
2.73 KB
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Numerical_flowrates_5x1arrays_Confinement07_Figure5.csv
6.35 KB
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Numerical_flowrates_5x1arrays_Porosity063_Figure5.csv
7.75 KB
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Numerical_flowrates_5x5arrays_Comparison_with_experiments_Figure2.csv
6.17 KB
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Numerical_flowrates_5x5arrays_Confinement03_Figures3and5.csv
7.38 KB
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Numerical_flowrates_5x5arrays_Confinement05_Figures3and5.csv
7.41 KB
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Numerical_flowrates_5x5arrays_Confinement07_Figures3and5.csv
7.42 KB
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Numerical_flowrates_5x5arrays_Porosity063_Figures3and5.csv
7.50 KB
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README.md
21.63 KB
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Velocity_measurements_rectangularchannel_Constant_Flowrate_Varying_Height_FigureS1.csv
4.29 KB
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Velocity_measurements_rectangularchannel_Constant_Height_Varying_Flowrate_FigureS1.csv
5.51 KB
Abstract
Hair-covered appendages serve a variety of purposes in Nature, from chemical sensing and particle capture on the antennae of a crustacean to drag generation on bristled wings. Despite their large porosity, these finite porous structures experience very little flow through at low Reynolds numbers. This flow regime, characterized by large viscous boundary layers around the hairs, is known as the paddle or rake regime. As the Reynolds number of the flow increases, so does the relative flow rate through the array, which corresponds to the deflection and sieve regimes. Confining structures, such as the animal body or larger hairs, have been hypothesized to focus the flow on the hair-covered region. We investigate the influence of confinement on the flow through and around an array of cylinders, using a combination of experiments and numerical simulations. Experimentally, we vary the hair spacing, channel dimension, and flow rate and measure the velocity field using Particle Image Velocimetry. After comparing the results of finite element analysis with the experimental data, we numerically investigate a broader range of system geometries and flow parameters. Our results show that the confinement focuses the flow in the array and shifts the domains of existence of the three regimes. We present an analytical model that relies on the permeability of rectangular slits to predict the relative flow rate through and around the array. The model is in quantitative agreement with the numerical results, demonstrating that the flow through the array increases with increasing confinement, while the flow angle decreases. These results should provide insight into the morphology of hairy surfaces and have implications in the design of bio-inspired flow sensors and filters.
Dataset DOI: 10.5061/dryad.xksn02vwk
Description of the data and file structure
The files list the flow rates measured experimentally with PIV and estimated from COMSOL simulations. Each file contains the parameters of the experiment or simulation (channel and array geometry, and Reynolds numbers of the flow, calculated for a cylinder), and the obtained flow rates. The flow rates are measured in the mid-plane, across the channel Q, in the region of the array with no cylinders Q_0. The flow rates entering the array Q_in and exiting the array Q_out are also reported.
Files and variables
File: Velocity_measurements_rectangularchannel_Constant_Height_Varying_Flowrate_FigureS1.csv
Description: Typical PIV measurements recorded at the start of an experiment to ensure the flow is at steady state. All data sets are recorded in the mid-plane. Only the flow rate in the channel varies
Variables
- w1 (mm): width of the channel
- y1 (mm): vertical position in the channel, y = 0 is the midplane
- Q1 (ml/min): flow rate in the channel
- x1(mm): horizontal position in the channel along x-axis
- u1 (mm/s): velocity in the z-direction
- w2 (mm): width of the channel
- y2 (mm): vertical position in the channel, y = 0 is the midplane
- Q2 (ml/min): flow rate in the channel
- x2(mm):horizontal position in the channel along x-axis
- u2 (mm/s): velocity in the z-direction
- w 3(mm): width of the channel
- y3 (mm): vertical position in the channel, y = 0 is the midplane
- Q3 (ml/min): flow rate in the channel
- x3(mm): horizontal position in the channel along x-axis
- u3 (mm/s): velocity in the z-direction
- w 4(mm): width of the channel
- y4 (mm): vertical position in the channel, y = 0 is the midplane
- Q4 (ml/min): flow rate in the channel
- x4(mm): horizontal position in the channel along x-axis
- u4 (mm/s): velocity in the z-direction
- w5 (mm): width of the channel
- y5 (mm): vertical position in the channel, y = 0 is the midplane
- Q5 (ml/min): flow rate in the channel
- x5(mm):horizontal position in the channel along x-axis
- u5 (mm/s): velocity in the z-direction
- w6 (mm): width of the channel
- y6 (mm): vertical position in the channel, y = 0 is the midplane
- Q6 (ml/min): flow rate in the channel
- x6(mm):horizontal position in the channel along x-axis
- u6(mm/s): velocity in the z-direction
File: Velocity_measurements_rectangularchannel_Constant_Flowrate_Varying_Height_FigureS1.csv
Description: Typical PIV measurements recorded at the start of an experiment to ensure the flow is at steady state. All data sets are recorded in different horizontal planes. The flow rate in the channel is set.
Variables
- w1(mm): width of the channel
- y1 (mm):vertical position in the channel, y = 0 is the midplane
- Q1 (ml/min):flow rate in the channel
- x1(mm): horizontal position in the channel along x-axis
- u1 (mm/s): velocity in the z-direction
- w2 (mm):width of the channel
- y2 (mm):vertical position in the channel, y = 0 is the midplane
- Q2 (ml/min):flow rate in the channel
- x2(mm): horizontal position in the channel along x-axis
- u2(mm/s): velocity in the z-direction
- w3 (mm): width of the channel
- y3 (mm):vertical position in the channel, y = 0 is the midplane
- Q3 (ml/min): flow rate in the channel
- x3(mm): horizontal position in the channel along x-axis
- u3(mm/s): velocity in the z-direction
- w4 (mm):width of the channel
- y4 (mm):vertical position in the channel, y = 0 is the midplane
- Q4 (ml/min):flow rate in the channel
- x4(mm): horizontal position in the channel along x-axis
- u4(mm/s): velocity in the z-direction
- w5 (mm):width of the channel
- y5 (mm):vertical position in the channel, y = 0 is the midplane
- Q5 (ml/min):flow rate in the channel
- x5(mm): horizontal position in the channel along x-axis
- u5(mm/s): velocity in the z-direction
File: Experimental_flowrates_Figure2.csv
Description: Experimental flow rates measured using PIV for different channel and array geometries. All data sets are recorded in the mid-plane.
Variables
- w1 (mm): width of the channel
- delta1 (mm): center to center spacing between cylinders
- nxn1: number of cylinders per row x number of cylinders per column
- C1: array confinement
- phi1: porosity of the array
- Re1: Reynolds number of the flow
- U1: Average velocity in the channel
- q 1: flow rate in the channel (3D)
- Q1(PIV): flow rate across channel in midplane
- std deviation Q1(PIV): standard deviation of the flow rate across channel in midplane
- Qin1(PIV): flow rate entering the array in midplane
- std deviation Qin1(PIV): standard deviation of the flow rate entering the array in midplane
- w2 (mm): width of the channel
- delta2(mm): center to center spacing between cylinders
- n2xn2: number of cylinders per row x number of cylinders per column
- C2:array confinement
- phi2: porosity of the array
- Re2: Reynolds number of the flow
- U2:Average velocity in the channel
- q2: flow rate in the channel
- Q2(PIV):flow rate across channel in midplane
- std deviation Q2(PIV): standard deviation of the flow rate across channel in midplane
- Qin2(PIV):flow rate entering the array in midplane
- std deviation Qin2(PIV):standard deviation of the flow rate entering the array in midplane
- w 3(mm): width of the channel
- delta3(mm): center to center spacing between cylinders
- n3xn3: number of cylinders per row x number of cylinders per column
- C3:array confinement
- phi3: porosity of the array
- Re3: Reynolds number of the flow
- U3: Average velocity in the channel
- q3: flow rate in the channel
- Q3(PIV):flow rate across channel in midplane
- std deviation Q3(PIV): standard deviation of the flow rate across channel in midplane
- Qin3(PIV): flow rate entering the array in midplane
- std deviation Qin3(PIV):standard deviation of the flow rate entering the array in midplane
- w 4(mm): width of the channel
- delta4 (mm): center to center spacing between cylinders
- n4xn4: number of cylinders per row x number of cylinders per column
- C4: array confinement
- phi4: porosity of the array
- Re4: Reynolds number of the flow
- U4: Average velocity in the channel
- q4: flow rate in the channel
- Q4(PIV):flow rate across channel in midplane
- std deviation Q4(PIV): standard deviation of the flow rate across channel in midplane
- Qin4(PIV): flow rate entering the array in midplane
- std deviation Qin4(PIV):standard deviation of the flow rate entering the array in midplane
File: Numerical_flowrates_5x1arrays_Porosity063_Figure5.csv
Description: Numerical flow rates measured COMSOL for a line of 5 cylinders, at different confinements for a porosity of 0.63. All data sets are recorded in the mid-plane.
Variables
- w1(mm):width of the channel
- delta1(mm):center to center spacing between cylinders
- nx1_1: number of cylinders in the line
- C1: array confinement
- phi1: porosity of the array
- Re1: Reynolds number of the flow
- U1: Average velocity in the channel
- q 1: flow rate in the channel
- Q 1(FEA):flow rate across channel in midplane
- Qin1(FEA): flow rate entering the array in midplane
- w2(mm):width of the channel
- delta2(mm):center to center spacing between cylinders
- nx1_2:number of cylinders in the line
- C2: array confinement
- phi2: porosity of the array
- Re2: Reynolds number of the flow
- U2: Average velocity in the channel
- q2: flow rate in the channel
- Q2(FEA):flow rate across channel in midplane
- Qin2(FEA): flow rate entering the array in midplane
- w3(mm):width of the channel
- delta3(mm):center to center spacing between cylinders
- nx1_3:number of cylinders in the line
- C3: array confinement
- phi3: porosity of the array
- Re3: Reynolds number of the flow
- U3: Average velocity in the channel
- q3: flow rate in the channel
- Q3(PIV):flow rate across channel in midplane
- Qin3(PIV): flow rate entering the array in midplane
- w4(mm):width of the channel
- delta4(mm):center to center spacing between cylinders
- nx1_4:number of cylinders in the line
- C4: array confinement
- phi4: porosity of the array
- Re4: Reynolds number of the flow
- U4: Average velocity in the channel
- q4: flow rate in the channel
- Q4(FEA):flow rate across channel in midplane
- Qin4(FEA): flow rate entering the array in midplane
File: Numerical_flowrates_5x1arrays_Confinement07_Figure5.csv
Description: Numerical flow rates measured COMSOL for a line of 5 cylinders, at a confinement of 0.7 and varying porosity. All data sets are recorded in the mid-plane.
Variables
- w_1(mm):width of the channel
- delta_1(mm):center to center spacing between cylinders
- nx1_1:number of cylinders in the line
- C_1: array confinement
- phi_1: porosity of the array
- Re_1: Reynolds number of the flow
- U_1: Average velocity in the channel
- q_1 : flow rate in the channel
- Q_1 (FEA):flow rate across channel in midplane
- Qin_1(FEA): flow rate entering the array in midplane
- w_2(mm):width of the channel
- delta_2(mm):center to center spacing between cylinders
- nx1_2:number of cylinders in the line
- C_2: array confinement
- phi_2: porosity of the array
- Re_2: Reynolds number of the flow
- U_2: Average velocity in the channel
- q_2: flow rate in the channel
- Q_2(FEA):flow rate across channel in midplane
- Qin_2(FEA): flow rate entering the array in midplane
- w_3(mm):width of the channel
- delta_3(mm):center to center spacing between cylinders
- nx1_3:number of cylinders in the line
- C_3: array confinement
- phi_3: porosity of the array
- Re_3: Reynolds number of the flow
- U_3: Average velocity in the channel
- q_3: flow rate in the channel
- Q_3(FEA):flow rate across channel in midplane
- Qin_3(FEA): flow rate entering the array in midplane
- w_4(mm):width of the channel
- delta_4(mm):center to center spacing between cylinders
- nx1_4:number of cylinders in the line
- C_4: array confinement
- phi_4: porosity of the array
- Re_4: Reynolds number of the flow
- U_4: Average velocity in the channel
- q_4: flow rate in the channel
- Q_4(FEA):flow rate across channel in midplane
- Qin_4(FEA): flow rate entering the array in midplane
File: Numerical_flowrates_5x5arrays_Confinement03_Figures3and5.csv
Description: Numerical flow rates measured COMSOL for an array of 5x5 cylinders, at a confinement of 0.3 and varying porosity. All data sets are recorded in the mid-plane.
Variables
- w_1(mm):width of the channel
- \delta_1(mm):center to center spacing between cylinders
- nxn_1: number of cylinders per row x number of cylinders per column
- C_1: array confinement
- \phi_1: porosity of the array
- Re_1: Reynolds number of the flow
- U_1: Average velocity in the channel
- q_1 : flow rate in the channel
- Q_1 (FEA):flow rate across channel in midplane
- Qin_1 (FEA): flow rate entering the array in midplane
- Qout_1 (FEA): flow rate exiting the array in the z direction in midplane
- w_2(mm):width of the channel
- \delta_2(mm):center to center spacing between cylinders
- nxn_2:number of cylinders per row x number of cylinders per column
- C_2: array confinement
- \phi_2: porosity of the array
- Re_2: Reynolds number of the flow
- U_2: Average velocity in the channel
- q_2: flow rate in the channel
- Q_2 (FEA):flow rate across channel in midplane
- Qin_2 (FEA): flow rate entering the array in midplane
- Qout_2 (FEA): flow rate exiting the array in the z direction in midplane
- w_3(mm):width of the channel
- \delta_3(mm):center to center spacing between cylinders
- nxn_3:number of cylinders per row x number of cylinders per column
- C_3: array confinement
- \phi_3: porosity of the array
- Re_3: Reynolds number of the flow
- U_3: Average velocity in the channel
- q_3: flow rate in the channel
- Q_3 (FEA):flow rate across channel in midplane
- Qin_3 (FEA): flow rate entering the array in midplane
- Qout_3 (FEA): flow rate exiting the array in the z direction in midplane
- w_4(mm):width of the channel
- \delta_4(mm):center to center spacing between cylinders
- nxn_4:number of cylinders per row x number of cylinders per column
- C_4: array confinement
- \phi_4: porosity of the array
- Re_4: Reynolds number of the flow
- U_4: Average velocity in the channel
- q_4: flow rate in the channel
- Q_4 (FEA):flow rate across channel in midplane
- Qin_4 (FEA): flow rate entering the array in midplane
- Qout_4 (FEA): flow rate exiting the array in the z direction in midplane
File: Numerical_flowrates_5x5arrays_Confinement07_Figures3and5.csv
Description: Numerical flow rates measured COMSOL for an array of 5x5 cylinders, at a confinement of 0.7 and varying porosity. All data sets are recorded in the mid-plane.
Variables
- w_1(mm):width of the channel
- \delta_1(mm):center to center spacing between cylinders
- nxn_1:number of cylinders per row x number of cylinders per column
- C_1: array confinement
- \phi_1: porosity of the array
- Re_1: Reynolds number of the flow
- U_1: Average velocity in the channel
- q_1 : flow rate in the channel
- Q _1(FEA):flow rate across channel in midplane
- Qin_1(FEA): flow rate entering the array in midplane
- Qout_1(FEA): flow rate exiting the array in the z direction in midplane
- w_2(mm):width of the channel
- \delta_2(mm):center to center spacing between cylinders
- nxn_2:number of cylinders per row x number of cylinders per column
- C_2: array confinement
- \phi_2: porosity of the array
- Re_2: Reynolds number of the flow
- U_2: Average velocity in the channel
- q_2: flow rate in the channel
- Q_2(FEA):flow rate across channel in midplane
- Qin_2(FEA): flow rate entering the array in midplane
- Qout_2(FEA): flow rate exiting the array in the z direction in midplane
- w_3(mm):width of the channel
- \delta_3(mm):center to center spacing between cylinders
- nxn_3:number of cylinders per row x number of cylinders per column
- C_3: array confinement
- \phi_3: porosity of the array
- Re_3: Reynolds number of the flow
- U_3: Average velocity in the channel
- q_3: flow rate in the channel
- Q_3(FEA):flow rate across channel in midplane
- Qin_3(FEA): flow rate entering the array in midplane
- Qout_3(FEA): flow rate exiting the array in the z direction in midplane
- w_4(mm):width of the channel
- \delta_4(mm):center to center spacing between cylinders
- nxn_4:number of cylinders per row x number of cylinders per column
- C_4: array confinement
- \phi_4: porosity of the array
- Re_4: Reynolds number of the flow
- U_4: Average velocity in the channel
- q_4: flow rate in the channel
- Q_4(FEA):flow rate across channel in midplane
- Qin_4(FEA): flow rate entering the array in midplane
- Qout_4(FEA): flow rate exiting the array in the z direction in midplane
File: Numerical_flowrates_5x5arrays_Confinement05_Figures3and5.csv
Description: Numerical flow rates measured COMSOL for an array of 5x5 cylinders, at a confinement of 0.5 and varying porosity. All data sets are recorded in the mid-plane.
Variables
- w_1(mm):width of the channel
- \delta_1(mm):center to center spacing between cylinders
- nxn_1:number of cylinders per row x number of cylinders per column
- C_1: array confinement
- \phi_1: porosity of the array
- Re_1: Reynolds number of the flow
- U_1: Average velocity in the channel
- q _1: flow rate in the channel
- Q _1(FEA):flow rate across channel in midplane
- Qin_1(FEA): flow rate entering the array in midplane
- Qout_1(FEA): flow rate exiting the array in the z direction in midplane
- w_2(mm):width of the channel
- \delta_2(mm):center to center spacing between cylinders
- nxn_2:number of cylinders per row x number of cylinders per column
- C_2: array confinement
- \phi_2: porosity of the array
- Re_2: Reynolds number of the flow
- U_2: Average velocity in the channel
- q_2: flow rate in the channel
- Q_2(FEA):flow rate across channel in midplane
- Qin_2(FEA): flow rate entering the array in midplane
- Qout_2(FEA): flow rate exiting the array in the z direction in midplane
- w_3(mm):width of the channel
- \delta_3(mm): center to center spacing between cylinders
- nxn_3:number of cylinders per row x number of cylinders per column
- C_3: array confinement
- \phi_3: porosity of the array
- Re_3: Reynolds number of the flow
- U_3: Average velocity in the channel
- q_3: flow rate in the channel
- Q_3(FEA):flow rate across channel in midplane
- Qin_3(FEA): flow rate entering the array in midplane
- Qout_3(FEA): flow rate exiting the array in the z direction in midplane
- w_4(mm):width of the channel
- \delta_4(mm):center to center spacing between cylinders
- nxn_4:number of cylinders per row x number of cylinders per column
- C_4: array confinement
- \phi_4: porosity of the array
- Re_4: Reynolds number of the flow
- U_4: Average velocity in the channel
- q_4: flow rate in the channel
- Q_4(FEA):flow rate across channel in midplane
- Qin_4(FEA): flow rate entering the array in midplane
- Qout_4(FEA): flow rate exiting the array in the z direction in midplane
File: Numerical_flowrates_5x5arrays_Porosity063_Figures3and5.csv
Description: Numerical flow rates measured COMSOL for an array of 5x5 cylinders, at a porosity of 0.63 and varying confinement. All data sets are recorded in the mid-plane.
Variables
- w_1(mm):width of the channel
- \delta_1(mm):center to center spacing between cylinders
- nxn_1:number of cylinders per row x number of cylinders per column
- C_1: array confinement
- \phi_1: porosity of the array
- Re_1: Reynolds number of the flow
- U_1: Average velocity in the channel
- q _1: flow rate in the channel
- Q_1(FEA):flow rate across channel in midplane
- Qin_1(FEA): flow rate entering the array in midplane
- Qout_1(FEA): flow rate exiting the array in the z direction in midplane
- w_2(mm):width of the channel
- \delta_2(mm):center to center spacing between cylinders
- nxn_2:number of cylinders per row x number of cylinders per column
- C_2: array confinement
- \phi_2: porosity of the array
- Re_2: Reynolds number of the flow
- U_2: Average velocity in the channel
- q_2: flow rate in the channel
- Q_2(FEA):flow rate across channel in midplane
- Qin_2(FEA): flow rate entering the array in midplane
- Qout_2(FEA): flow rate exiting the array in the z direction in midplane
- w_3(mm):width of the channel
- \delta_3(mm):center to center spacing between cylinders
- nxn_3:number of cylinders per row x number of cylinders per column
- C_3: array confinement
- \phi_3: porosity of the array
- Re_3: Reynolds number of the flow
- U_3: Average velocity in the channel
- q_3: flow rate in the channel
- Q_3(FEA):flow rate across channel in midplane
- Qin_3(FEA): flow rate entering the array in midplane
- Qout_3(FEA): flow rate exiting the array in the z direction in midplane
- w_4(mm):width of the channel
- \delta_4(mm):center to center spacing between cylinders
- nxn_4:number of cylinders per row x number of cylinders per column
- C_4: array confinement
- \phi_4: porosity of the array
- Re_4: Reynolds number of the flow
- U_4: Average velocity in the channel
- q_4: flow rate in the channel
- Q_4(FEA):flow rate across channel in midplane
- Qin_4(FEA): flow rate entering the array in midplane
- Qout_4(FEA): flow rate exiting the array in the z direction in midplane
File: Numerical_flowrates_5x5arrays_Comparison_with_experiments_Figure2.csv
Description: Numerical flow rates measured COMSOL for an array of 5x5 cylinders, with the same porosities and confinements as the experiments. All data sets are recorded in the mid-plane.
Variables
- w_1(mm):width of the channel
- \delta_1(mm):center to center spacing between cylinders
- nxn_1:number of cylinders per row x number of cylinders per column
- C_1: array confinement
- \phi_1: porosity of the array
- Re_1: Reynolds number of the flow
- U_1: Average velocity in the channel
- q _1: flow rate in the channel
- Q _1(FEA):flow rate across channel in midplane
- Qin_1(FEA): flow rate entering the array in midplane
- w_2(mm):width of the channel
- \delta_2(mm):center to center spacing between cylinders
- nxn_2:number of cylinders per row x number of cylinders per column
- C_2: array confinement
- \phi_2: porosity of the array
- Re_2: Reynolds number of the flow
- U_2: Average velocity in the channel
- q_2: flow rate in the channel
- Q_2(FEA):flow rate across channel in midplane
- Qin_2(FEA): flow rate entering the array in midplane
- w_3(mm):width of the channel
- \delta_3(mm):center to center spacing between cylinders
- nxn_3:number of cylinders per row x number of cylinders per column
- C_3: array confinement
- \phi_3: porosity of the array
- Re_3: Reynolds number of the flow
- U_3: Average velocity in the channel
- q_3: flow rate in the channel
- Q_3(FEA):flow rate across channel in midplane
- Qin_3(FEA): flow rate entering the array in midplane
- w_4(mm):width of the channel
- \delta_4(mm):center to center spacing between cylinders
- nxn_4:number of cylinders per row x number of cylinders per column
- C_4: array confinement
- \phi_4: porosity of the array
- Re_4: Reynolds number of the flow
- U_4: Average velocity in the channel
- q_4: flow rate in the channel
- Q_4(FEA):flow rate across channel in midplane
- Qin_4(FEA): flow rate entering the array in midplane
Code/software
N/A
Access information
Other publicly accessible locations of the data:
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Data was derived from the following sources:
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